A Generalization of the Pignistic Transform for Partial Bet

  • Authors:

  • Thomas Burger;Alice Caplier

  • Affiliations:

  • CNRS, Lab-STICC, Centre de Recherche Yves Coppens, Université Européenne de Bretagne, Université de Bretagne-Sud, Vannes cedex, France F-56017;Gipsa-Lab, Domaine universitaire, Saint Martin d'Hères cedex, France 38402

  • Venue:
  • ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
  • Year:
  • 2009

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Abstract

The Transferable Belief Model is a powerful interpretation of belief function theory where decision making is based on the pignistic transform. Smets has proposed a generalization of the pignistic transform which appears to be equivalent to the Shapley value in the transferable utility model. It corresponds to the situation where the decision maker bets on several hypotheses by associating a subjective probability to non-singleton subsets of hypotheses. Naturally, the larger the set of hypotheses is, the higher the Shapley value is. As a consequence, it is impossible to make a decision based on the comparison of two sets of hypotheses of different size, because the larger set would be promoted. This behaviour is natural in a game theory approach of decision making, but, in the TBM framework, it could be useful to model other kinds of decision processes. Hence, in this article, we propose another generalization of the pignistic transform where the belief in too large focal elements is normalized in a different manner prior to its redistribution.